We made FWD:Everyone (https://www.fwdeveryone.com) for this exact problem. It works via a Gmail add-on, so you can upload an email thread after it's over without having to grant OAuth access to your inbox. It makes these threads taggable and searchable within your company, and formats them to make them look beautiful.

The advantage over just copying everything to a mailing list is that most conversations aren't worth archiving, so having conversations be opt-in after the fact keeps the signal-to-noise ratio much higher than it would otherwise be.

We're still a very small platform, but since we're completely bootstrapped and grew 34x year-over-year in the past year, we're not going anywhere. :-)